Spatial non-uniformity in digitally printed images is a commonly observed phenomenon exhibited by almost all printers. As illustrated in FIG. 1, for a given color channel digital input level to the printer, the printed color at first and second horizontal locations x1, x2 is not the same, and/or the printed color at first and second vertical locations y1, y2 is not the same. This color non-uniformity or “color drift” as a function of space on the paper or other recording medium often appears as serious image quality defects. These defects include, e.g., one-dimensional defects such as banding or streaks or two-dimensional defects such as mottle. It has been observed that the appearance of most non-uniformity defects depends on image content and color and intensity levels. Because the rendered color is a function of the halftoning method employed, spatial non-uniformity is also halftone dependent. Additionally, many high-end printers are equipped with multiple halftone screens which necessitates that any halftone dependent spatial correction method be repeated for each halftoning method.
To maintain consistent color reproduction, it is necessary to characterize the non-uniformity of each printer device so that corresponding color adjustments can be applied at the time of printing to compensate. Previous methods require printing and measuring test patches that are halftone dependent, which requires that patches be printed and measured for each available halftone method. For a xerographic engine equipped with multiple halftone screens, this method can be very time consuming to characterize each color channel for each halftone screen, as these measurements increase linearly with the number of halftone screens. Often, the design of printed test patches also varies depending upon the halftone screen, which leads to still more complexity. As such, it has been deemed desirable to develop a halftone independent apparatus and method for correction of spatial non-uniformities.
Co-pending U.S. patent application Ser. No. 11/343,656 filed Jan. 31, 2006 assigned to Xerox Corporation and entitled “Halftone Independent Color Drift Correction” is hereby expressly incorporated by reference into this specification. This prior application discloses one or more halftone independent methods and apparatus for compensating for temporal or media color drift in a printer. In particular, a first true tone response curve (TRC) for a color channel is determined when the printer is in a first state (first time or first media). A first predicted tone response curve for the color channel is also determined when the printer is in the first state. A second predicted tone response curve for the color channel is determined when the printer is in a second, color-drifted state relative to the first state, i.e., at a later time or using a different paper or other recording medium. A second true tone response curve for the color channel is then mathematically estimated using the first true tone response curve, the first predicted tone response curve, and the second predicted tone response curve. The first and second predicted tone response curves are generated using a 2×2 printer model as disclosed below.
The use of the 2×2 printer model provides a reliable and efficient proxy for full color characterization such as described, e.g., in S. Wang, K. Knox and C. Hains, “Digital Color Halftones” Digital Color Handbook, Chapter 6, CRC Press. Full color characterization is a time consuming operation that is preferably avoided in most xerographic printing environments. Simpler color correction methods based on 1-dimensional (1-D) TRC calibration for each of the individual color channels are usually sufficient and are easier to implement. The 1-D TRC calibration approach is also well-suited for use of in-line color measurement sensors, but is typically halftone dependent. In general, for each color channel C and for each halftone method H, a series of test patches are printed in response to N different digital input levels which requires C×H×N test patches, because the test patches must be printed for each halftone method. It has been found in practice that N must not be too small (e.g., N=16 is usually too small) because the TRC for each halftone method is typically not a smooth curve, due to dot overlapping and other microscopic geometries of the printer physical output. Existing methods for 1-D calibration, being halftone dependent, are measurement-intensive, and are not practical for in-line calibration, especially in print engines equipped with multiple halftone screens.
Previously, Wang and others have proposed a halftone independent printer model for calibrating black-and-white and color printers. This halftone independent printer model is referred to as the two-by-two (2×2) printer model and is described, e.g., in the following U.S. Patents, all of which are hereby expressly incorporated by reference into this specification: U.S. Pat. Nos. 5,469,267; 5,748,330; 5,854,882; 6,266,157 and 6,435,654. The 2×2 printer model is also described in the following document that is also hereby expressly incorporated by reference into this specification: S. Wang, “Two-by-Two Centering Printer Model with Yule-Nielsen Equation,” Proc. IS&T NIP14, 1998.
The monochrome 2×2 printer model is explained briefly with reference to FIGS. 2A, 2B and 2C (note that in FIGS. 2A, 2B, 2C the grid pattern is shown for reference only). FIG. 2A illustrates an example of an ideal halftone printer output pattern IHP (which can represent, e.g., a single pixel P of an image), where none of the solid color ink/toner dots ID overlap each other (any halftone pattern can be used and the one shown is a single example only); practical printers are incapable of generating non-overlapping square dots as shown in FIG. 2A. A more realistic dot overlap model is the circular dot model shown in FIG. 2B for the pattern HP (the halftone pattern HP of FIG. 2B corresponds to the halftone pattern IHP of FIG. 2A). These overlapping dots D in combination with optical scattering in the paper medium create many difficulties in modeling a black-and-white printer (or a monochromatic channel of a color printer). The dots ID, D are shown by shaded regions to comply with Patent Office drawing rules, but those of ordinary skill in the art will recognize that the dots ID, D are solid color (black or other color) regions.
In a conventional approach such as shown in FIG. 2B, the location for each dot D is defined by a rectangular space L of the conceptual grid pattern G, and each location L is deemed to have a center coincident with the center of the dot D output (or not output) by the printer. Because the grid G is conceptual only, according to the 2×2 printer model, the grid G can be shifted as shown in FIG. 2C as indicated at G′ so that the printer output dots D of the pattern HP are then centered at a cross-point of the grid G′ rather than in the spaces (the spaces are labeled L′ in the shifted grid G′). Although the halftone dot pattern HP for FIGS. 2B and 2C is identical, overlapping details within each of the rectangular spaces L′ of the grid G′ of FIG. 2C are completely different as compared to the spaces L of the grid G of FIG. 2B. More particularly, there are only 24=16 possible different overlapping dot patterns for the 2×2 model shown in FIG. 2C, while there are 29=512 different overlapping dot patterns in a conventional circular dot model as shown in FIG. 2B.
The 16 possible different overlapping dot patterns of FIG. 2C can be grouped into seven categories G0-G6 as shown in FIG. 2D, i.e., each of the 16 possible different overlapping dot patterns of a pixel location L′ associated with the model of FIG. 2C can be represented by one of the seven patterns G0-G6 of FIG. 2D. The patterns G0 and G6 represent solid white and solid black (or other monochrome color), respectively. The pattern G1 is one of four different equivalent overlapping patterns that are mirror image of each other, as is the pattern G5. Each of the patterns G2, G3, G4 represents one of two different mirror-image overlapping patterns. Therefore, in terms of ink/toner color coverage (gray level), all pixels (located in the rectangular spaces L′ of the conceptual grid pattern G′) of each of the seven patterns G0-G6 are identical within a particular pattern G0-G6. In other words, each pattern G0-G6 consists of only one gray level and this gray level can be measured exactly.
The 2×2 printer model as just described can be used to predict the gray level of any binary (halftone) pattern, because any binary pattern such as the halftone pattern of FIG. 2C can be mathematically modeled as a combination of the seven patterns G0-G6, each of which has a measurable gray level as just described. In other words, after the seven test patches G0-G6 are printed and the gray (color) level of each is measured once, the gray level of any binary halftone pattern can be predicted mathematically and without any additional color measurements.
For example, the halftone pattern HP of FIG. 2C is shown in FIG. 3, along with its corresponding 2×2 based model M, wherein the gray level of each space L′ of the grid G′ is represented by one of the seven 2×2 patterns G0-G6 that has a corresponding color output pattern/coverage for its dots D′. Thus, for example, for the location L′00 of the binary pattern HP, the 2×2 pattern G1 has dots D′ with corresponding color coverage as indicated at M′00, while for the location L′50 of the pattern HP the 2×2 pattern G3 has dots D′ with corresponding color coverage as shown at M′50, and for the location L′66 of halftone pattern HP there is no color (blank coverage) which corresponds to the 2×2 test patch G0 as indicated at M′66 of the model M, etc. As such, any binary pattern of ink/toner dots can be modeled as a combination of the 2×2 patterns G0-G6 by selecting, for each dot D′ of the binary pattern, the one of the 2×2 patterns G0-G6 that is defined by dots D′ having color coverage in the locations L′ that equals the color coverage of the corresponding halftone pattern location L′.
When a binary pattern HP is represented by a model M comprising a plurality of the patterns G0-G6, the gray level output of the binary pattern HP can be estimated mathematically, e.g., using the Neugebauer equation with the Yule-Nielsen modification, as follows:
      G    AVG          1      /      γ        =            ∑              i        =        0            6        ⁢                  n        i            ⁢              G        i                  1          /          γ                    where Gi, i=0 to 6 is the measured gray level of the respective 2×2 patterns G0-G6, ni is the number of dots of the corresponding 2×2 pattern occurring in the binary pattern, and γ is the Yule-Nielsen factor, a parameter which is often chosen to optimize the fit of the model to selected measurements of halftone patches. Details of such an optimization are given in S. Wang, K. Knox and C. Hains, “Digital Color Halftones” Digital Color Imaging Handbook, Chapter 6, CRC Press, 2003.For example, the average gray level of the binary pattern of FIG. 2B/FIG. 2C can be estimated as:GAVG=(7G01/γ+25G11/γ+7G21/γ+3G31/γ+3G41/γ+3G51/γ+G61/γ)γ
The color 2×2 printer model can be described in a similar manner. The color 2×2 printer model can predict the color appearance of binary patterns for a given color printer and the color accuracy of the prediction is high for printers with relatively uniform dot shapes, such as inkjet printers. However, xerographic printers usually do not generate uniform round-shape dots for isolated single pixels and the dot overlapping is more complicated as compared to inkjet dot output. As such, the color 2×2 printer model applied to a xerographic printer will typically yield larger prediction errors.
The 2×2 test patches G0-G6 shown in FIG. 2D are theoretical. For real-world use, each of the test patches G0-G6 can be printed in a variety of different ways. The test patches G0′-G6′ shown in FIG. 4 illustrate an example of one possible real-world embodiment for printing the seven patterns G0-G6, respectively. The present development is described hereinbelow with reference to printing and measuring the color of the real-world 2×2 test patches G0′-G6′, and those of ordinary skill in the art will recognize that this is intended to encompass printing and measuring the color of any other test patches that respectively represent and correspond to the patterns G0-G6 in order to satisfy the 2×2 printer model as described herein. It is not intended that the present development, as disclosed below, be limited to use of the particular style of test patches G0′-G6′ or any other particular embodiment of the 2×2 patterns G0-G6. In general, for the 2×2 printer model to hold, the shape of the printer output dots D′ must be symmetric in the x (width) and y (height) directions, and each dot D′ should be no larger than the size of two output pixel locations L′ in both the x and y directions. The dots D′ need not be circular as shown. It should be noted that the 2×2 test patches G0-G6 and G0′-G6′ as shown in FIGS. 2D and 4, are binary in the sense that the “shaded” regions as shown in the patent drawings are “solid” color (black or other color channel) but to comply with Patent Office rules, solid black regions are not used in the patent drawings.